A port-Hamiltonian approach to formation control using bearing measurements and range observers

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In this paper we consider the problem of formation control using measurements of the bearings between vehicles. We design our system using port-Hamiltonian theory and the bondgraph modelling technique. Our approach builds upon the architecture presented in [22], which relied on partial measurements of relative position rather than position measurements with respect to an inertial frame. The previous work used a generalised form of the image Jacobians employed in image-based visual servo (IBVS) control literature to compute the desired control forces. However, the implementation of these measurement Jacobians requires unknown information about the relative positions of the vehicles. A key contribution of this paper is that we show how a depth observer can be integrated into the design to overcome this problem for the case where bearing measurements are available. Assuming that a single distance measurement is also available, we can specify a rigid goal formation in terms of the available measurements of relative positions. For this system, we prove local convergence to the desired configuration. We then provide a discussion regarding the implementation, and suggest that in practice, the distance measurement may be unnecessary. This discussion is supported by simulation results.